In this article, we investigate the information-theoretical performance of a cooperative orthogonal frequency division multiplexing (OFDM) system with imperfect channel estimation. Assuming the deployment of training-aided channel estimators, we derive a lower bound on the achievable rate for the cooperative OFDM system with amplify-and-forward relaying over frequency-selective Rayleigh fading channels. The bound is later utilized to allocate power among the training and data transmission phases. Numerical results demonstrate that the proposed power allocation scheme brings between 5 and 19% improvement depending on the level of signal-to-noise ratio and relay locations.